Semiclassical regime of Regge calculus and spin foams

Abstract

Recent attempts to recover the graviton propagator from spin foam models involve the use of a boundary quantum state peaked on a classical geometry. The question arises whether beyond the case of a single simplex this suffices for peaking the interior geometry in a semiclassical configuration. In this paper we explore this issue in the context of quantum Regge calculus with a general triangulation. Via a stationary phase approximation, we show that the boundary state succeeds in peaking the interior in the appropriate configuration, and that boundary correlations can be computed order by order in an asymptotic expansion. Further, we show that if we replace at each simplex the exponential of the Regge action by its cosine -as expected from the semiclassical limit of spin foam models -then the contribution from the sign-reversed terms is suppressed in the semiclassical regime and the results match those of conventional Regge calculus.

Simpler way of imposing simplicity constraints

“…In this article we calculate the asymptotic behaviour of the amplitude of a 4-simplex for both the DL model as well as the new model proposed in [20]. We find first that the DL model's asymptotics turn out to be the same as the EPRL-FK model [21][22][23][24][25][26][27][28][29][30], as was expected. Next, we study the asymptotics of the new model and find that due to non-trivial cancellations on-shell, it has the same 1st order behaviour, giving Regge Calculus [31].…”

Invited review: The new spin foam models and quantum gravity

“…The previous result together with the fact that the EPRL amplitude for γ < 1 is a product of SU (2) amplitudes with the same n in the coherent state representation (88) implies the asymptotic formula for the vertex amplitude to be given by the unbalanced square of the above formula [167], namely was calculated in [189] and it was shown to produce a result in agreement with that of Regge calculus [190,191] in the limit γ → 0.…”

Semiclassical limit of 4-dimensional spin foam models

“…This should be contrasted with what was achieved in the context of the Barret-Crane model, where only one or two 4-simplices were considered [8]. An extension of these results to more 4-simplices seemed increasingly complicated (see [42] for a very recent discussion of this in the context of Regge calculus). The second fact to be noticed is that the Immirzi dependence drops out in the semiclassical limit.…”